Lemma 4.34  [1]}
Let \(G\)  be a reductive group acting linearly on polarised schemes \((X,\mathcal {L}_X)\)  and \((Y,\mathcal {L}_Y)\)  and let \(f : X \rightarrow Y\)  is a \(G\) -equivariant morphism such that \(f^*\mathcal {L}_Y \cong \mathcal {L}_X\) . Then \(f^{-1}(Y^{G-ss}) \subset X^{G-ss}\) , and if \(f\)  is quasi-affine we also have \(f^{-1}(Y^{G-s}) \subset X^{G-s}\) .

